I had the same problem. I habe weird nipples and my right one is really small and baby girl has a little bird tongue. The doctor told me to play with it some to get it erect and she was able to latch better.
Definitely contact the consultant if you can because they are going to have the best advice but it may just be a trial and error process and she may just prefer the left side. 🤷‍♀️

I've heard lactation consultants are helpful, I can only say to keep trying! trust your body & your baby! The first MONTH was the hardest for us, are u holding your breast up with one hand while she feeds? I found that helpful.
Maybe before u latch her on to it you could try going into the bathroom and just expressing some milk out with your hand over the sink or in the shower, maybe get a little bit going for her?

Can you see a lactation consultant?